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This book is an advancement of the Age-Structured Matrix by introduced by Leslie P.H. in 1945. It gives an Extension that was not foreseen by Leslie, where individuals exhibit Migration characteristics. The text is ideal in the study of population structures for any Undergraduate or Graduate studies both in the areas of Mathematical Biology and Population Ecology. An application has been made to estimation of population size and structure of whale sharks. Only one application has been discussed, but the model is sufficient for wide applications in population dynamics.